One-to-One Relation

An One-to-One Relation is a Binary Relation where an Argument Value is only in the Relation with one other Argument Value (and vice versa).

• AKA: Injective Relation.
• Context:
  • It can be a Reflexive Relation.
  • ...
• Example(s):
  • A Property Relation can be one. E.g. for unique identifiers.
  • A Successor Relation.
  • One gene expresses one protein. “The Pseudomonas aeruginosa oprB gene encodes the carbohydrate-selective OprB porin, which translocates substrate molecules across the outer membrane to the periplasmic glucose-binding protein."
  • A passport number refers to one person and one person has at most one passport number. (note though that not every person has a passport).
  • “Brian Mulroney was succeeded by Kim Campbell who was succeeded by Jean Chrétien."
  • ...
• Counter-Example(s):
  • a One-to-Many Relation.
  • a Many-to-Many Relation.
• See: Relation, One-to-One Function.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Injective_function
  • In mathematics, an injective function is a function which associates distinct arguments with distinct values.
  • An injective function is called an injection, and is also said to be a one-to-one function (not to be confused with one-to-one correspondence, i.e. a bijective function).
  • A function f that is not injective is sometimes called many-to-one. (However, this terminology is also sometimes used to mean "single-valued", i.e. each argument is mapped to at most one value.)
  • A monomorphism is a generalization of an injective function in category theory.

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